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Homework Help: Electric field at the center of a semicircle

  1. Apr 1, 2013 #1
    1. The problem statement, all variables and given/known data

    See the image attached

    2. Relevant equations
    Ex = (Kλ/R)*∫3/2ππ/2(cosθ)dθ

    3. The attempt at a solution

    Ey cancels because there is an equal amount of force in both y directions. For the electric field on the x axis, the above equation can be used.

    Given that λ=Q/L

    λ=(85x10^-9 C)/(0.1 m)

    R = L/θ
    =(0.1 m)/(3/2π - π/2)

    E = ((8.85x10^-9)(8.5x10^-7)/0.03183)*pi
    = 7.424640507894822×10^-13

    This is not correct. Please help! Thanks in advance.

    Attached Files:

  2. jcsd
  3. Apr 1, 2013 #2
    take an element dx at θ with width dθ
    then integrate from 0 to∏
  4. Apr 1, 2013 #3
    Haha! I just realized my mistake as soon as you posted! Thank you very much!

    To be clear for anyone who looks at this post for help in the future,

    Ex = (Kλ/R)*∫3/2ππ/2(cosθ)dθ

    Since the integral from pi/2 to 3pi/2 is not going to have the correct coordinates to give you the correct length, you must integrate from 0 to pi since the shape is a semicircle (half a circle) or from 0 to pi on a trigonometric circle.

    When you integrate from 0 to pi/2, the charge for half the semicircle is 240072.2588752749

    Multiply that number by two, and the correct answer is:

    4.9×105 N/C

    Thanks again!
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